Hi axi0m. 440 can be hardened to a very high strength but of course it isn't ductile at all at higher strength levels. If it breaks, it will break catastrophically. Material for pressure systems is best if it yields significantly before breaking. Not to say you shouldn't use it, but you might consider other materials.
First, a better understanding of the stress the material is under would help. I've attached a graph for your particular application that looks at the hoop stress level in the material as a function of radius. Note that it starts at r=1" where stress is 125 ksi and quickly drops off to 40 ksi at r=2" and 25 ksi at r=3". That's because there is a tremendous compressive load on the ID that translates to a hoop stress. For a ductile material with a yield below 125 ksi, you might get a bit of yielding on the ID but not much. The OD material won't yield. Generally, the safety factor isn't applied to this 'artificially' high hoop stress on the ID. For thick walled vessels and piping, it isn't unusual to find the pressure exceed the yield. For example, there are numerous manufacturers of "cone and thread" type high pressure tube and fittings. This is a very thick wall 300 series stainless steel tube that's been work harded. The end of the tube is cut into a cone shape and threaded, with a nut that holds it into a fitting. The tube can withstand pressure up to 100,000 psi or even higher but I don't think the yield stress of the material is that high. Doing a calculation on the 1/4" tube you find a hoop stress on the ID of 113 ksi, and this is just work hardened 316. A couple of manufacturers include http://www.newport-scientific.com/" . The point here is that the kind of pressure you're looking at achieving isn't all that unusual, and 440C or other high tensile strength materials is typically not used. Generally a work hardened 316 or 304 is the most common. You might also consider Nitronic which is a very high strength austenitic stainless steel that can be work hardened, but will still retain considerable ductility. The austenitic stainless steels will also have better corrosion resistance, though I don't understand what you need that for quite honestly. I'll take your word for it.
Regarding the ends, having generous radiuses is always a plus to minimize stress concentrations. You might consider posting a drawing to show what it is.
Regarding fatigue, (http://mmd.sdsmt.edu/fatigue_text/Image289.jpg" ) is a typical curve, but is valid for most iron based metals like the 300 or 400 series stainless steels and all carbon steels. We see this graph starts at 10^3 cycles with a limit of S/Su = .9 which means the stress it takes to break the material under completely reversed stress is 90% of the ultimate tensile strength after being exposed to 1000 cycles. I wouldn't put too much thought into this, the point is that if your material isn't exposed to more than 1000 cycles (or even 10,000 cycles), and as long as you're looking at "normal" factors of safety to yield of at least 1.5, you really don't have to consider fatigue. If your material is under much higher levels of stress or the number of cycles exceeds at least 1000 cycles, you should consider how fatigue may affect your material. Do you expect more than 1000 cycles on the material?
I wonder why you need stainless though. Are you concerned about corrosive attack? If so, you may need to retest the unit after a few uses just to assure yourself the material isn't being degraded by some kind of corrosive affect. I'd be surprised if it were, but I don't know what your situation is. Perhaps you could better describe what your concerns are.
